Abstract We introduce a family of algebraic curves over 𝔽 q 2 n (for an odd ) and show that they are maximal. When = 3, our curve coincides with the 6 -maximal has been found by Giulietti Korchmáros recently. Their (i.e., case 3) is first example maximal proven not to be covered Hermitian curve.

We study linear complementary pairs (LCP) of codes (C, D), where both belong to the same algebraic code family. especially investigate constacyclic and quasicyclic LCP codes. obtain characterizations for quasi-cyclic Our result extends characterization dual (LCD) cyclic given by Yang Massey. observe that when C D are constacyclic, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊥</sup> equivalent each other. Hence, security parameter min(d(C),...

Abstract The Giulietti-Korchmáros (GK) function field is the first example of a maximal which not subfield Hermitian over same constant field. generalized GK C n was later introduced by Garcia, Güneri and Stichtenoth shown to be too. In present article we determine automorphism group We prove that all automorphisms fix unique rational place at infinity they are exactly lifts H ⊂ infinite

We give a general lower bound for the minimum distance of $q$-ary quasi-cyclic codes length $m\ell$ and index $\ell$, where $m$ is relatively prime to $q$. The involves distances constituent $\ell$ as well certain cyclic which are related fields over constituents defined. present examples show that sharp in many instances. also compare performance our against bounds Lally Esmaeili-Yari.

Following Jensen's work from 1985, a quasi-cyclic code can be written as direct sum of concatenated codes, where the inner codes are minimal cyclic and outer linear codes. We observe that nothing but constituents in sense Ling-Solé. This structure enables us to recover some earlier results on simple way, including one our recent which says with constituent 2-D In fact, we obtain generalization this result multidimensional The also yields lower bound minimum distance noted by Jensen, call...

The security parameter for a linear complementary pair (C, D) of codes is defined to be the minimum distances d(C) and d(D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">⊥</sup> ). Recently, Carlet et al. showed that if C D are both cyclic or 2-D codes, then, equivalent codes. Hence, simply d(C). We extend this result nD proof case based on trace representation which technical nontrivial generalize. Our generalization zero sets ideals corresponding

We introduce multidimensional analogues of quasi-cyclic (QC) codes and study their algebraic structure. demonstrate a concatenated structure for QC use this to prove that class is asymptotically good. also relate the new family convolutional codes. It known minimum distance provides natural lower bound on free show same relation holds between certain rank one 2-D related provide examples, which our sharp in some cases. present optimal Along way, we condition encoders codes, are equivalent...

We study complementary information set codes of length $tn$ and dimension $n$ order $t$ called ($t-$CIS code for short). Quasi-cyclic (QC) quasi-twisted (QT) $t$-CIS are enumerated by using their concatenated structure. Asymptotic existence results derived one-generator fixed co-index QC QT depending on Artin's primitive root conjecture. This shows that there infinite families rate $1/t$ long with relative distance satisfying a modified Varshamov-Gilbert bound. Similar defined the new more...

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We give a new method in order to obtain Weil-Serre type bounds on the minimum distance of arbitrary cyclic codes over <emphasis emphasistype="italic"><formula formulatype="inline"><tex Notation="TeX">${\BBF}_{p^e}$</tex></formula></emphasis> length coprime formulatype="inline"> <tex Notation="TeX">$p$</tex></formula></emphasis>, where Notation="TeX">$e \ge 1$</tex></formula></emphasis> is an...

Linear codes with complementary-duals (LCD) are linear that intersect their dual trivially. Multinegacirculant of index $2$ LCD characterized algebraically and some good found in this family. Exact enumeration is performed for indices 2 3, all $t$ a special case the co-index by using concatenated structure. Asymptotic existence results derived class such one-generator have power two means Dickson polynomials. This shows there infinite families multinegacirculant relative distance satisfying...